Internal problem ID [3592]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 862.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}+\left (x -y+a \right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.103 (sec). Leaf size: 44
dsolve(x*diff(y(x),x)^2+(a+x-y(x))*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\left (c_{1}^{2}+c_{1}\right ) x}{-c_{1}-1}-\frac {c_{1} a}{-c_{1}-1} \\ y \relax (x ) = c_{1} \sqrt {x}+a -x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 60
DSolve[x (y'[x])^2+(a+x-y[x])y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+\frac {a}{1+c_1}\right ) \\ y(x)\to \left (\sqrt {a}-i \sqrt {x}\right )^2 \\ y(x)\to \left (\sqrt {a}+i \sqrt {x}\right )^2 \\ \end{align*}